How to design a part to fit exactly onto an existing 3D model?
This is what I would do:

Start by importing the file and aligning it with the grid. Aligning with the x-y-z axes will make tranformations easier.


Next, go into Edit mode and select the good half of the model by pressing b and clicking/dragging your cursor . Preferably, you should do this after smoothing out the scanning imperfections so that you don't have to clean each side of the model independently.


Use Shift+d to duplicate the selected vertices and p to separate them from the original mesh. The new mesh is no longer closed, and you will need to close off the opened edge of the mesh before performing any boolean operations. Select the outer ring of vertices, and use Shift+F to fill the empty space.


Using a combination of mirror transformations, rotating, and moving, place the closed mesh in the desired position on the other side of the model. You might have to move the new mesh down slightly or decrease its scale by a tiny amount, so that none of the new mesh's faces hide faces along the top of the original mesh.


The new mesh is now overlapping the broken edge of the original mesh and needs to be trimmed to fit.


In Object mode, select the new mesh (blue) first, hold Shift, and then select the original mesh (red). Press w, and click Difference. Blender will subtract the original mesh from the new mesh and introduce a third mesh containing the difference. The third mesh (colored green here) should closely fit the original mesh's broken edges.




I can add a .blend file later today if it will help. Cleaning and accurately scaling the mesh will probably be the most challenging part of this project.